If secθ +tanθ=x, then tanθ is -

If secθ +tanθ=x, then tanθ is - Correct Answer (x2-1)/2x

Step - by - step explanation:Given : sec θ + tan θ = x …….. (1)By using an identity , sec² θ - tan² θ = 1(sec θ + tan θ)(sec θ - tan θ) = 1[By using identity , a² - b² = (a + b) (a - b) ]x (sec θ - tan θ) = 1(sec θ - tan θ) = 1/x ……….(2)On Subtracting eq 1 & 2, sec θ + tan θ - (sec θ - tan θ) = (x - 1/x)sec θ + tan θ - sec θ + tan θ) = (x - 1/x)2 tan θ = (x - 1/x)2 tan θ = (x² - 1)/xtan θ = (x² - 1)/2xHence, the value of tan θ is (x² - 1)/2x.